Create a Family Emergency Plan and do a few practice runs with and without your kids and pets. Ensure your pet's training includes quick evacuation, recall, quiet, and other potentially life-saving commands. Have a get-home bag and First Aid kit in your vehicle and a bugout bag for each family member (including pets).
It may sound extreme but being stranded with your kids and dog on the side of the road and unable to open electric windows sucks. The water, snacks, and weather gear you pre-packed could save a life.